MFG model with a long-lived penalty at random jump times: application to demand side management for electricity contracts

Clémence Alasseur (), Luciano Campi (), Roxana Dumitrescu () and Jia Zeng ()
Additional contact information
Clémence Alasseur: EDF R &D and Finance for Energy Market Research Centre (FIME)
Luciano Campi: University of Milan
Roxana Dumitrescu: King’s College London
Jia Zeng: King’s College London

Annals of Operations Research, 2024, vol. 336, issue 1, No 17, 569 pages

Abstract: Abstract We consider an energy system with n consumers who are linked by a Demand Side Management (DSM) contract, i.e. they agreed to diminish, at random times, their aggregated power consumption by a predefined volume during a predefined duration. Their failure to deliver the service is penalised via the difference between the sum of the n power consumptions and the contracted target. We are led to analyse a non-zero sum stochastic game with n players, where the interaction takes place through a cost which involves a delay induced by the duration included in the DSM contract. When $$n \rightarrow \infty $$ n → ∞ , we obtain a Mean-Field Game (MFG) with random jump time penalty and interaction on the control. We prove a stochastic maximum principle in this context, which allows to compare the MFG solution to the optimal strategy of a central planner. In a linear quadratic setting we obtain a semi-explicit solution through a system of decoupled forward-backward stochastic differential equations with jumps, involving a Riccati Backward SDE with jumps. We show that it provides an approximate Nash equilibrium for the original n-player game for n large. Finally, we propose a numerical algorithm to compute the MFG equilibrium and present several numerical experiments.

Keywords: Demand side management; Real-time pricing; Mean-field games; Mean-field control; Delay; Riccati BSDE with jumps; Stochastic maximum principle (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10479-023-05270-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-023-05270-0

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-023-05270-0

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().